Long-haul communication systems require optical amplifiers to compensate for fiber loss. Current systems use erbium-doped or Raman fiber amplifiers. These amplifiers are examples of phase-insensitive amplifiers (PIAs), which produce signal gain that is independent of the signal phase. In principle, phase-sensitive amplifiers (PSAs) could also be used. The potential advantages of PSAs include, but are not limited to, noise reduction (See, e.g., R. Loudon, “Theory of noise accumulation in linear optical-amplifier chains,” IEEE J. Quantum Electron. 21, 766-773 (1985)) the reduction of noise- and collision-induced phase (See, e.g., Y. Mu and C. M. Savage, “Parametric amplifiers in phase-noise-limited optical communications,” J. Opt. Soc. Am. B 9, 65-70 (1992), and frequency (See, e.g., H. P. Yuen, “Reduction of quantum fluctuation and suppression of the Gordon-Haus effect with phase-sensitive linear amplifiers,” Opt. Lett. 17, 73-75 (1992)) fluctuations, and dispersion compensation (See, e.g., R. D. Li, P. Kumar, W. L. Kath and J. N. Kutz, “Combating dispersion with parametric amplifiers,” IEEE Photon. Technol. Lett. 5, 669-672 (1993)). Previous papers (See, e.g., C. J. McKinstrie and S. Radic, “Phase-sensitive amplification in a fiber,” Opt. Express 12, 4973-4979 (2004); and C. J. McKinstrie, M. G. Raymer, S. Radic and M. V. Vasilyev, “Quantum mechanics of phase-sensitive amplification in a fiber,” Opt. Commun. 257, 146-163 (2006)) showed that degenerate four-wave mixing (FWM) in a randomly birefringent fiber (RBF) produces phase-sensitive amplification (PSA), provided that the signal frequency (ω0) is the average of the pump frequencies (ω−1 and ω1). Degenerate scalar and vector FWM are illustrated in FIGS. 1(a) and 1(b), respectively. In degenerate scalar FWM (inverse modulation interaction), γ−1+γ1→2γ0, where γj represents a photon with frequency ωj. In degenerate vector FWM, (degenerate phase conjugation), γ−1+γ1→γ∥γ⊥, where the subscript 0 was omitted for simplicity. If one assumes that each interaction involves only the aforementioned pumps and signal, then each interaction produces PSA with the classical properties of a one-mode squeezing transformation.
FWM processes are driven by pump- and signal-induced nonlinearities and are limited by dispersion-induced wave number shifts. If the pump frequencies differ significantly, strong dispersion prevents other FWM processes from occurring and the preceding assumption is valid. However, it is difficult to phase lock pumps with dissimilar frequencies, which are usually produced by two separate lasers. In contrast, it is easy to phase lock pumps with similar frequencies, which can be produced by one laser and a phase modulator. However, if the pump frequencies are similar, dispersion is too weak to counter nonlinearity and other FWM processes occur.
A previous paper on scalar FWM (See, e.g., C. J. McKinstrie and M. G. Raymer, “Four-wave-mixing cascades near the zero-dispersion frequency,” Opt. Express 14, 9600-9610 (2006)) showed that, if the pump frequencies are comparable to the zero-dispersion frequency (ZDF) of the fiber, a cascade of product waves (harmonics) is produced. These harmonics limit the level, and modify the phase sensitivity, of the signal gain. Accordingly, there is a need for a way to achieve phase sensitive amplification without the problems caused by frequency cascades.